Braking of wheels



March 4', 1930. A. Y. DODGE 1,749,022

BRAKING OF WHEELSl Filed Feb. 23, 1927 4 Sheets-Sheet 1 A7' TURA/EX.v

March 4, 1930. Y A Y, DODGE 1,149,022 l BRAKING OF WHEELS Filed Feb. 25,1927 4 Sheets-Sheet 2 Fig-.4.

March 4, 1930.

A. Y. DODGE 1,749,022

BRAKING OF WHEELS 4l Sheets-Sheet 3 Filed Feb. 23,1192? 4 Sheets-Sheet 4A. Y. DODGE BRAKING WHEELS Filed Feb. 25, 1927 March 4, '1930.

A TTRNE )i f abona-The aai- -UNITED STATES F SOUTH BEND, INDIANA,ASSIGNOR T0 '.BNDIX BRAKE 00k- Letters Patent d o. 1,604,394-,

which it is hung, may

Patented Mar. 4, 1930 PATENT OFFICE ADIIL Y. DODGE,

PANY, 0l' CHICAGO, ILLINOIS, A COBPORATIDN 0F ILLINOIS :maxima orwHimr-.s

Application med February 23, 1927. Serial No. 1470,138.

This invention relates toV brakes for swiveled wheels and Iis disclosedin connection with a front wheel brake for automobile wheels of the ty edisclosed in United States granted October 26, 1926, on my applicatlon.i

A front wheel ofan automobile is not necessarily vertical. Its uppervportion may tiltl to the outside, and the king pin, `or swivel, on tiltcorrespondingly to the inside so that its axis intersects the Wheelplane at or near the point of contact of the wheel with the ground. Thekingpin is often also tilted somewhat, backward through the so-'calledcaster angle. brake in such -a wheel is operated generally by meansincluding a universal joint apwhich The turning of the wheel, after thebrake is set,

' unless one of lthe axes of the universal joint e is collinear with theking pin axis at this time, will in itself change lthe conditions underwhich the joint operates and can be ard to tighten and yon the otherfront loosen.

ans

ranged to cause thebrake on one front wheel ,.ffPr'evious to the presentinvention, such akes have been constructed in two ways, mentioned above,inwhlch an axis of the universal joint is collinear with the king pinaxis-when the brake is set, and the second in 'which an axis of thejoint, though not'colflinear with the; king pin axis, appears insubstantially the 'same nearly yverticalpla'ne as'the king pin axis whenlviewed fromv-- the 'sideafter the brake has been set. In theivrstconstruction'the turning'bf` the wheelfdoes not afe'ct the con'dition ofthe brake'.""'In1the second construction, the brake on fronesidetightens, and that on the other side'loosens, and these effects areequal'in magnitude on both sides, `assuming the wheels to vhave turnedthrough the sameV angle. There is va 'decidedadyiinta'ge in having-thebrake lon the outside if ont wheel loose in-goingfaround a 'cornerf'nfthat the danger of skidding is diminished, and the axes of the jointhave been generally so arranged as to bring this The wheel to j brakingforce exerted by the operator was then applied to theother three wheels,and since the inside front wheel brake had been tightened by the turningof that wheel, this unbalanced the ei'ect of the brakes o n the threeheavily braked wheels, and under some conditions in itself created atendency to skid.

' The object of the present invention isto preserve the advantageinherent in the relief of the outside front wheel brake while avoidingthe danger of skidding dueto the unbalancing Aof the braking action onthe other three wheels, and accordingly to socon'- struct the brakeapparatus that the relief of the outside front wheel brake takes placemuch more rapidly than the tightening of the inside front wheel brake,as-these wheels areA turned, thus minimizing the diiierence ,inthebraking action on the three heavily v braked wheels.

I have found that this can be accomplished by making the vertical axisof the universal joint tilt out of the nearly or quite vertical planein'which the king pin axis is seen from the side when the brakes areset. This unbalances the effects on the twol front wheels which are dueto their turning to the side. The relative effectson the front wheelscan be varied between wide limits by varying the amount of thislaterally apparent tilt in accordance with the theory which I shallexplain in the annexed sjgieciiication.F I am thus enabled to relievethe outside front wheel brake to any desired ydegree withoutcorrespondingly tightening the brake on the inside front wheel, and thusunbalancing to a prejudicial extent the braking action on the threeremaining wheels.

In ,the accompanying drawings, which showa'preferred embodiment of theinven# tion, i

Fig. 1 is a partly sectional front elevation of the right front wheel ofanautomobile, and also shows a cross-section on the line I-Iof Fig. 4;

Fig. 2 is a section on Fig 1A; v. l g l Fig. 3 isa section on the lineIII-III of Fig. l; l l .f

the line II-II of vio.

Fig. 4 is a section on the line IV--IV of Fig. 1;

Figs. 5 to 8 are diagrams illustrating the mathematical theory to bedeveloped;

Fig. 9 is a diagram illustrating the set-up.

chosen forI illustration v fFig. 10 shows graphically the brakingresults derived from the set-up shown in Flg. 9; Fig. 11 'isa diagram bymeans of which practical factory problems in brake setting maybe solved;

' Fig. 12 is a diagram generally illustrating j thephenomena discussedherein and Fig. 13 is a view similarr to Fig. 4 showing the parts in thebrake-set ,positiom In the arrangement selected for illustration, thebrake acts on `a right front'wheel rotatably mounted on a knuckle 10swivelled by a king pin 12 on\the end of an axle 14 supmember `28ttinginto a key slot .in the end of a camshaft 30. f

The camshaft 30 is journaled in acylindrical bore in a bearing orsupport 32 bolted to a backing plate 34 mounted iixedly on theknuckle10.

The inner endof the camshaft 30 is bored i out conically or sphericallyat 35, to give as milch play as possible to a control shaft '36. havinga rounded and flattened end swiveled by a pin 38 between two members 40having inner fiat surfaces engaging the attened end of the shaft, andhaving cylindrical outer surfaces journaled in a normally horizontalcrossv bore or bearing inthe end of the camshaft 30.

'Ihe control shaft-36 is iiuted to be embraced by a splitclamp formed onthe end of an arm 42, thus providing for angular adjustment of the armby loosening the clamp.. The bottom ofthe arm is formed with a sphericalsocket or seat for-a. member 44, which may be integral with, or backedby,

a nutl 46 threaded on a link 48 operated by the pedal connections and anopening150 intersecting t ber 44.

e seat for mem- The elements 30, 36, 38, 40 constitute in "thus `turningthe cam 26-to crowd the wheel lmanner that the cam loosens the brake onan assing through 16, as described in the patent referred to.

Fig. 1 shows the parts as they are with the machine going straight aheadwi the brakes ofl', the vertical axis lying approximately in a verticallplane transversel to the car.l The control"andcamlshafts are showncollinear but there is often a few degrees variation in this'ali-nementdue to the Alimitations ofl space on the chassis and its verticalposition underload. LK x The setting of the brake is accomplished by-rp'ulling'the arm 42 backward, rotating the shafts 36 and 30 and theuniversal joint, the brake 'shoesto the drum,`as shown in Fig. 13. Theosition of the vertical axis is there indicated y a line marked 38. o YAssuming vthat the control shaftis held fast when the wheel isturned bythe steering mechanism, a small rotation of the cam shaft to thebacking/ plate 34, due to the the vertical axis with the king brakes, arotation of the control shaft of 6-8 is necessary, the vertical axisover toward the observer of Fig. 1. yPrevious devices of this characterhave been so arranged that the verticalaxis after being so throwncomesinto the transverse vertical plane, to the wheel pin axis.

relatively plane and containing the king Withsuch an arrangement when 1sturned, the parts move in such the turning of the Wheel causes.

fact that j of the' joint is not ycollinearpin axis. In order to set thesov which will turn the top of or a plane perpendicular outside wheeland tightens the brake on an v insde whe'el, these effects being equal.

enabled to vary these actions relatively, that is to-cause the outsidewheel brake to loosen faster or slower than the insidewheel brake. Ihave found that the .relation ofthe tightening and loosening effectsdepends upon the position of the vertical axis at the time the wheel isturning, that is, on the 4position to which it is thrown by the act ofsetting the brakes. If the to? of the vertical axis is thrown forward oand outside of the king pin axis in setting the brake an outside wheelbrake will loosen faster than an inside one tightens; ifit is thrownbackward of and 'outside f the king pin axis an inside brake willtighten faster than an outside one loosens.

I will now show how the effect maybe determined exactly in any givencase. i

It will be necessary first to establish a number of mathematicalconsiderations, upon-which the analysis depends, and I will first derivegeneral Formul (11) and 12) below, relatlng to revolution directioncosines Z, m, n. v

We shall needto recall'the following relations from analytic geometry.-

means of the present invention I am about an axis -passlng through theorigln and having the l. If l, An, are the direction cosines of a me uz2+m2+n2-=1 (A) If two lines are given by'their direction cosines,theangle'between them is given by order, as above, as an'be seen fromFig. 6. For suppose that Y1 is in the OXY plane.

Then amr-L Then in Fig. 6 a1`1= cos X 0 X1,

a2'2'=cos Y 0AY1, a83=cos ZOZI, are all positive, and since as theX1Y1Z1 set of axes rotates in any way, the numerical characterisf ticsof the system change continuously, theA 1o Let cosines of thetransformation (D) on the one hand and the direction cosines of the axisaround which the equivalent rotation takes place andthe amount ofrotation on the other hand; and vice versa. By means of thisrelationship the effect ofthe turning of the Wheel on the braking can bedetermined with accuracy, as will be seen.

In the following discussion al1 lineswill be regarded as directed andtheir direction cosines will refer to their positive ends, and positiverotation about a line will be such as represented in Fig. 5, The'axesused will be i right handed, such that a positive rotation about the Zaxis will turn X toward Y, etc.

The as in (D) are the direction cosines of the two sets of axesrelatively to each other, according to the following table:

Since 0X1 is perpendicular to OY1 and OZ1;

' that K= 1. The positive sign is-tlre correct one when the. as arearranged infv cyclical value K +1 must apply universally, and

. we have, in the determinantof the cosines,

each element equal to its own first minor. This determinant is then @12@1a @22 @2a @sa Any such change of axes as We are discussing can beeffected by three consecutive rotations about the axes in turn, so thatof these nine as only three are independent.

We proceed to express them in terms of three i independent quantities.

A.By addition and substractin of (I) and (J) v (l'i`-a11 agg a33) Theparentheses on the right of each of (K) are either both positive or bothnegative. If those in the first equation 'are negative, their sum, 1a11,is negative, which is impossible,

since an is a cosine. jSimilarly those i'n the second equatlon arepositive. Therefore We may put 4a 2 1 -la a a @naal i @12@22 'l' @maza vla? 1 -iai ai ag; (L) @naarl' @12@ a2+@13@33= 0 4a22= 1.- ani @2a-@s3whence Mahl-@randagi I @il @12 G13 l.: K: 1 (G) @22am @azazs @2:4131@33021 @21032 @31022 l A as will be seen from the following i alf alf-l- (21.32 l K2[ (andas @32023)2 'l' (023031 0330202 'i' (021032@311122) 2l The quantity in the brackets is the Asquare Assume A v ofthe sine of theangle between -OYl .and OZ1, alza l daz: 4020s by (C) andis therefore equal to. unity, so 23 S2 4a0a1 (M) where the signs chosenfor the square roots remain to be justified. Then Similarly, or byadvancing subscripts cyclically, we get the setofdouble-dierent-subscript as in terms of the single subscript as.a23=2(a;a3a0a1) a31=2(w1a,woa2) and from (L) vtherefore forms aconsistent system of direction cosines. l

The assumption in (M) does not determine the signs of the singlesubscript as, -but only the signs of their products. By comparison withthe terms of (D), the signs of the products can be determined, and thentwo sets of signs can be determined for the single sub- ,Script as, eachthe opposite Vof the other.

These, as will be seen, simply give the two ends of the axis, andy Sinceghz) is on the unit sphere: 'w2+y2+z2=w1=K2[16a14+ieafazwiealzam, and ISince the point (agg, z) did not move,it

lies on the axis of rotation, and since it is at unit distance from theorigin, the above` values of y, Aand z are the direction cosines of theaxis of rotation, Z, m, n.

We find the angle, 0, of rotation, as follows:

will lie on a great circle ofthe sphere angu-` larly distant, around theaxis, by 0 from the plane. In Fig. 7 OP is the axis of rotation, and OMSis the plane through the axis and OZ. The planes OMR and OMNmake anglesof 0 on each side of OMS. OR and ON are the intersections of theseplanes with OXY, and R and N are taken at unit distance from O. MR andMN are takenperpendicular to OP, and RSN is erpendicular to OS. Theprojection, along P, of the langle 5:6, on the XY plane, is =ROSC B y(4) and by (16), proved later, the projectlon angle y, of the POS planeon the the corresponding angles of rotation. OX? Plane 1S gwen by Wewill next ind the axis of rotation imt 1 a 2 cos YOP 4 f plied in (D).Take a point y, a) on the an 7* Z a, c0s XOP unit sphere,l whichtransforms into itself Also Y p v under the transformation (D). We thenRS have tan Mw m (al1-1)'l'" tan azz-113+ (az2 1)y+ @232:0 anw -I-uazy-l- (asa- 1)z=0 M S4 )OSM- Z P as f whence cos cos 0 al-lag -I- w32m y z .(1) Y (022 1) (033- 1) @3202s @23031- (flas- 1) (G21)amaez'aa1(a22 1) andremembering that any element in (H) is .Hence equalto its own first minor, we have,

:n y z au azz aaa l 1 a12 G21 als 'l' @si Substituting from (N), (0);and from (P), for w;

A Us

158.11 1km 158.11 i0' (5) For the point R;

=Gs (WM), y=sin (v-q), 2=f0 (6) isp For the point N;

. substitute for Then, by (P) putting N =c2+1 25 Then, puttin 4N), 0),we have Mos (wiegeen (wma-10 1 m f and R is moved to N b the rotation.Substitute (6) and 7) in the third of (D):

alo

@twv-dts Ea. 2 (8) Put I f cot =c (9),

ansiosa not, let (a, y) be a.

@int is it.-"rhen the coordinates of (w, y, 2S

and (ms/'1, .21) referred to a system of parallel axs through.

ssii) vIn. the following investigation, the origin I will firstbe'taken' at the center ofthe u'ni- 4 versal joint, with "the Z' axisvertically 1 =Sin29=a12+ 0122 "l 0132+ Z, m, n for the direction cosinesof the axis, P, in (4)', and substituting in .fkfelz-mzwo l(11)..

Formulae (4) and (8) give' the direction cosines of the axis, and theamount,of the rotation (D) in terms of the singlel subscript as, andformula(L) gives the single subscript as in terms of the doublesubscript asl of (D). We can thus determine. the axis and amount of.rotation corresponding to any` given transformation D.

On the other hand if we are given' the axis and the amount oftherotation, Formula (11) gives the double subscript as for the equlvalenttransformation (D).

`Heretofore we have assumed the axis of rotation to passthrough theorigin. If it does @falla-m2351- tanta upward, the X axis horizontal andpointing straight to-the outside right ofthe car, and the Y axisperpendicular to both and exi tending forward. The king pin is notvertical. Its to slopes some 5-8 inward and` about 2&0 ackward. Itsposition and that of other vparts will ordinarily be given by elevationsandplans in drawings', and it is necessary to establish formulaeforrelating a line so given to the coordinate axes.

Let P (Fig. 10) be the intersection of the positive end of the line inquestion with the unit sphere around the origin. The direction coslnesZ, m, n are marked on their arcs and the .spherical vangles at a, b, c"are all The projection angles, a', y, are marked in the figure.

' Then theequations of the line OP are zianz mmf (13) Of Col-irsethere'yare in reality only two independent.. equations here; multiplying them,

weobtain v v L l Atan;.;o tan tan y=`1 (14) Putting the equations in theform wev get the direction cosines of the line n: 41+ cot2+ www2/Hebentan By division-we obtain from (15) '7" l ZE j tan a-r tan -n tan 'y-l(16) From'such right triangles as XPc, XPbz,

we get The letters d, e, f will be used for the cosines of the controlshaft; i, m, n for those of the king pin; @,g, 1' for those of the camshaft; a, v, for those of the vertical axis; and s, t, u, for those ofthe horizontal axis. Letters relating tothe condition of things prior tothe brake setting will be marked with naught subscripts if their valueschange later; and letters relating to conditions after the wheelturning` will be marked with primes.

mm=cos a cos cos y=sin Formulae (l5) and (17) the latter of which` isadapted for logarithmic computation, give the direction coslnes of aline in terms of its ,projection angles, and Formula (16) gives theangles in terms of the cosines.

For the sake of completeness, the formula for the universal joint isincluded here, without proof, which can be found in text books onmechanism. The formula is tan =tan 0 cos 8 (19) where qS is the angleturned by the following shaft of the joint, 0 is the angle turned by thedriving shaft, both measured from the line of intersection of the planesof the driv-v ing and following axes, and is the acute angle between thedriving and following shafts.

We can thus determine the direction cosines of any line given on themachine drawings. We lshall have to so determine the cosines of the kingpin axis, the control and cam shafts and one of the axes of theuniversal joint. The position of the other axis willV then be determinedby mathematical considasinsinfus) f The condition of perpendicularitybetween the joint axes is 8A+ta+uv=0, (2O)v between the. horizontal axisand the cam 'shaft is .sp+tg+m'=0; (21) and the angle 511 that the camshaft has been turned by the wheel turning will be given by cos\/1=sa+tt+uu (2li/2) since this is the angle between the before andafter positions of the horizontal axis.

After obtaining the A', a', v corresponding to a wheel turning, we ndthe corresponding s', t', u by (20), (21) combined with w+ z'2+a'2=1(22) These Equations (20) (21) (22) can be solved as follows:

From (20) (21) s:t:u=rugv:pv-m:gtpp (23) and putting l verations, as itcannot be accurately enough determined in proper relation to the rstaxis from a drawing. The method of attack will be thus to determine thedirection cosines of all elements with the car going straight ahead andthe brake released; then to set the brake, and find 'the new cosines ofthe joint axes, and then to turn the wheel and find the new cosines ofthe horizontal axis, which will give us the angle the cam shaft has beenturned by the turning of the wheel. This vangle measures the releasingor tightening. To simplify the analytical work, instead of turning thewheel we shall turn the car in the opposite direction, an\ artificewhich will shorten the computation considerably.

#Kw4-w) =K(P# WV.) (25) u=K(Q --1w) t The signs must be determined byinspec- As will be seen, we shall ado t an artifice whereby g=o, so that(24) (25) ecome www (24') We shall regard th e king pin axis and the thefollowing proportion:

zontal axis as positive forward, andthe shafts as positive awayregardall these lines as extending Aone unit from the origin in theirpositive directions,

so that the coordinates of. their outside ends will equal theirdirection cosines.

In case the rotation, 0, of (1 2)"takes place around one of thecoordinate "axes, the transformation (12) -becomes very simple. Weshall, accordingly, after linding the cosines of the lines we need inthe XYZ system defined above, change the axes to an XYZ system so thatthe Z axis liesin the king pin axis, the XZ plane contains the camshaft, andthe Y' axis extends forwardly. ln order to effect thistransformation we shall need the cosines of the new axes with respect tothe old.

If 1r, p, a, are the `direction cosines of the XZ plane, we have as itsequation:

www0-F0 (26) and since the normal to this plane is perpen- I dicular tothe king pin axis and to the cam shaft, we have y as the equation of thenew XZ 'planepreferred to the XYZ axes. Its direction cosines 1r, p, a,which are those of the Y axls, satisfy l =sine ofangle between king pinand cam and we get its cosines, 1], t, in the ksame way:

from the joint.A We shall Xaxis, 4 front,'or positive end of the Y axis.

shaft 30 is 2 below the X axis, perpendicular` vber 2. The control shaft36 lies 2 whence The-tranSformaaoh-(35) ,will enable as to define allour lines with respectto the XYZ axes. The axisof rotation when thewheel turned' is now the Z axis. Therefore, in

(12), l='=m=o and Ilt=1. Bearing in mind that l the transformation (12)vbecomes, if A, pi, v,`

' are the cosinesl of the -line to be rotated, and

A', It', y', are its cosines lin its rotated position, simply l XY= cos@-p. sin 0 p.=)tsind+p.cos 0 (37)l Inasmuch as this transformation hasto be used for every angle of wheel turn investigated, the advantage ofthe transformation (35) is clear.

As a typical case takethe following: The king pin 12 of the right frontwheel slopes 2 backward (the caster angle) as seen from the side, orfrom the positive end of the and slopes 6 inward as seen fromthe whichis assumed to cambehind and 1 above the negative end of the X axis. SeeFig. 9 which shows the condition of things at the right front wheel asseen from the left rear of the car. The X and Y axes are positive awayfrom the observer. f

shaft, p

The direction cosines of the cam shaft 3l) are apparent directly fromthe figure.

I p=cos 2=0.9993908 I q=0 l'= cos 92= 0.03489950 to the wheel4 plane,

We next find the cosines l, m, @,-of' the king pin axis 12, from (14)and (15).

In solving the Equations (15) ,the non-symmetrical form is easiest touse, and this some- -times requires a cyclic permutation of the letters`in order to bring the two known angles under the radical. We have v wardZ. =3v54, seen from The cam a=92%, seen from X, measured from Y to- 8 vi l 1,749,022

cot2 a=`0.0019063 We now know the positions of all tle parts tan2=0.0110469 when the car is going Straight ahead, and will 1 1. set thebrake by turning the control shaft 8. 1p=m We could intreducethetransformation (35) 5 n: -Page3585@ first, but can save a little work bydeferring it. 70

Z=n tan 0.1044301 (39) We rst find the brake-setting position, A, ,1,m.=n cot a =.0.04338089 i v, 0f 'the vertical axis by (12). y

Next we nd the cosines, 41,9, f, of the conl c cot 4 14.300666 trolshaft 36. 75

. =271, y=182 y l(fm2 4 0.004865966 cot2 0.0008047 tanz vy=0.00:121951 1. z=d= -0;99 92888 bm= +0.08486768 3fm m=e= -0.08489419 m= 0.017428498 z= 0.9992888 a= f= +0.01744178 ma =f 0.0006086184 e= d tan y=-0.08489419 (40) y 181:- 14.289784 z2 0.9984782 f=d cot 0017441778 lcm=0.4990102 m2= 0001217804 Next we find the cosines of the joint axes. im:+0'2494291 n2: +0'0003042153- 85 One is arbitrary: We shall here assumethe c2= +204.50906 Na= +205.50801, Nm, 404291228, Nal, -10828774 Naz.;+0.5685982, N822 +208.51149, Na., +28.578851 25 I Na31= +0.9631634, Na32 -28.5807 85, N aaa +203.50966 90 an= +0.9999852, al. -0.002088097,a.. -0.005025946 a= +0.002706755, a.. Jf,0.9902799, a2, +0.1890618 an=+0.004686720, a.. 0.1890781, a.. +0.9902710 y (46) so i Then, by (12),(46) and (45) 95 ano alava -l- 0.01745215 0.00502518 0.0124269? p.= LMAO8281/0 =1 0.00004839 -l- 0.1390401 0.1390884 (47) v='as1/\0 aasvo0.0000818 l. 0.9901202 0.9902020 '35 horizontal shaft horizontal. iTherefore: x `We next find 8, t, u, the corresponding posi- 100 S tionof the horizontal axis. By (20), (21),

The vertical axis is perpendicular tothe hori- Y Tp.: A 105 40 zontalaxis, whence v o- 0+;.10- 1 +v00= 0, and 1')= 0.0004336950 I uo=0 (42) ypf= +0.9895988 l The vertical axis is also perpendicular to the l p1=9900325 v 110 control shaft. Therefore Y .l Y

i 10d+vf=0 and (48) PF-01390037 ,(Jrvozl l. (1w-w.)2= +0.9801644 osolving: 1 d l A ,.2= +0.01984`56 115 M=V=r "w (44) ,12+ (pv-m)2=+0.9995100 From (40) d K==tm= +1.0002451 120 7.28996 8= K-,.= 000485581'(1%132821397 y t=K(pv-r,\) `+0.9'902752 (47') 1 u=K(-p) -0.1890878 a12'5 1 7?:3283'1397 We are now read t y o urn the wheel about o=091745241 y the axis ofthe king pin, and will here intro- 0= 0- duce thetransformation (35). By (38),

f v= +0.9998477 (4,5.) (89) (90)', (81) f 1..0

I From '(38), (50) so +0.0015279-9.0015279=0 (5 1) l y simiiarlyfr0m(47),1 (750);

and, from (47) (750) 59 It will be carried through for two angles ofthat the projection of the vertical axis of the XY plane after the brakeis set, must be not less than 40o-45 froin the X axis. 0r, speakingroughly, this implies that the Ver- Ntioal-aariswliiustpoint about asmuch to the The result of the full computation (54) is shows the effectof. turning tiri wheel shown ra hicall in Fi l0 in which the farther asan outside wheel. e curve abscissa relpresent)7 anglesgof wheel-turn andshows`v the effect of turning the wheel back the ordinates of the curveOA represent outto the straight ahead position, and beyond 1t 20 sidelooeningd, tthose of the curve OB as an irtisldel livliel The urvs ggf,gli

re resen insi e 1 i eninm are ,exac y a i e u reverse y s1 a e E) FheWork teriniratinfr iii (54) is perfectly Peint E5 58 'C0/ille left 0f 0,Corresponde t0 general in its nature, aziid the method there theSPrlghl? ahead POSPU 0f the Wheel end 25 explained can be used insolving any probtle tlffhteleng 0I lolenmg effect Oltu'mlg lein. In theactual construction of brakes 1t t1e W leel 1S 01m Y @OmPamg le 0I' 1'is possible to simplify the process soniewhat. Page5115 ltlh tthflt .)fthsimt rgpllresgl' Supposethe brake has been set, land the 21P- lnpFllefl lilmlgnll fror'l 58o 03g' propriate computation carried throughto lllvs the 1005801 effec? on the outgid 30 (35), (51), (53). N owassulinethat the wheel h 1 d d t @1 h th has been turned until the ZaXls, the vertical ee n an OlxlmenFlF 1151 S lle anCnlZ ED 1 e se en mllSatil eefh 393 ilmig gom 58 to Qhows th given by' (16) z t tighteningeffect on the inside wheel. This segment, if turned end for end andyupside 35 tan ,:H down, is identical with Lthe curve OB, in i l 55) Fig.10. It is also identical with the segment *01823246 EC, running from 58to 93 on the right 0.1147538- 1588834 of Fig. 11. G f

In other words the curve 'H' shows by whence y-57" 48.8 40 It is obviousthatfgs the wheel turns either E53) gallc (elgSI- aedlg Way from du?1308113101131 hq henfotrle-Iml' are resulting from turiinfr the wheelbetween equal m mag-mtude on O't l S1( es 0 le'p une thesetw) oints Ifthe 'initial osition is to Now take this plane as the -XZ plane, withthe h h j P1 h 45 Yaxis pointing diagonally forward, we then ost aid tvVflsa- 1n Flg- 11a e brake e 1 3,- av F10. a11, therefore, can be usedto solve anv Y -problem in-which the vertical axls and the u o kinor pinaxis are'at an angle cos1v=12o26 50 1' 1 1 '50'2154313 irrespective ofhow the position ofthe control 20=+09902865 shaft and the'brake settingangle effected =o. (56)` -this. i 7': 01390421 It is obvious that, forthe given set-up, in 3:9 order to effect the result sought, that is, to.55 =1 make the outside wheel brake loosen substan- 0 tially faster thanthe inside one tightens, the and (37) becomes point E must separate twoparts of the curve i of substantially dilferent slope; that is, the @.OS0 v 7 point E must be at-least 40o-45 lout from 60 M, t Sm 9 (5 thecenter of the curve in Fig. 11. This means i front as to the side, inorder to produce the desiredv effect.

The above illustrated computation has 'been carried out to 7 decimalplaces, but 5 out. The 7th figure is of course not reliable.

i mining In the preceding analysis it is shown how to find the result ofa given Set-up, and the determination of the proper 'adjustment toroduce a specified effect can be found by a ew tentative computations,in which, for example, shaft is turned in setting the brake is varied.

In actual commercial production of numerous models of cars this methodof deterthe proper adjustments can be simplified. To this end, a familyof curves suich as DOC, Fig. 11, will be computed and plotted,corresponding to systematically varying angles between .the king pinaxis and the vertical axis. The curve DOC, as stated, is that derivedfrom the above discussed hypothetical set-up, where the angle inquestion, is about 1226-, having its cosine, v= +0.97 66190. The otherfour curves shown in Fig. 11 correspond to angles, T, of

semi angle 1, and with 2y, 5, 7 and 10, respectively, and are laid 0H inorder from the axis of abscissae.

Each such curve corresponds to a cone of its axis coincident with theking pin axis, and canbe used to show graphically .the braking e'ects ofthrowing the vertical axis to any position on its surface in setting thebrake and turning the wheel. The space characteristics of thel machine,determining the set-up, as shown in Fig. 9, determine the path in whichthe vertical axis must move in setting lthe brake. As the vertical axismoves over this path (the surface of a cone around the control shaft asaxis), it will pass into these f-'conical surfaces, one after the other.f

In working out this problem it will be advantageous to introduce thetransformation- (35) after the computation of (45), before rotating thecontrol shaft to set the brake. Then compute the positions of thevertical axis resulting from a series of rotations of the control shaft,say' every degree from -.1 to 10. The resulting series of vs willdetermine the corresponding curves in Fig. 11, and

the s and pis, as in (55) will determine the angles -y to be used withthe curves respectively. The proper segments of each curve will be takenolf and plotted as in Fig. 10, and the resulting Fig. 10 will be placedin order and examined. The characteristic sought (for example, makingtheoutside loosening twice the inside tightening for .a wheel turn of25) will be found to vary systematically through this series of Fig. 10,and the suitable one can be readily selected.

i The angle through which the control shaft the angle through which thecontrol i than the tightening of brake is set will lnoted in thatcompartment. This, of course,

must now be `turned in setting the brake is now known, and it remainsonly to relatively adjust the cam and brake shoes, and the members36-and 42 so that the brake will be so set by turning the control shaftthrough thisA The above investigation has lassumedfthe` vertical axisfixed' on the control shaft. Its

location on the cam shaft affords no difficulty in treatment. In thiscase it will be found that if the vertical axis is tilted forward andoutside the king pin, when the brake is set, the loosening of theoutside brake is less the inside; if the vertical axis is tiltedbackward and outside of the king pin vwhen the brake is set, theloosening of the outside brake is greater than the,

tightening of the inside.

Fig. 12 shows the effects of varying posi-v of the vertical axis.

tions ofthe upper end The centers of the circles represent the'king pin,and the view is taken along the king pin axis from above. Inlthis figurethe ex res'- sion LO TI is to be Vread Loosening o outside brake isgreater than tightening of inside brake. The other legends will be clearwithout explanation. It is understood', of course', that setting up thebrake so that the upper end of the vertical axis will be thrown to anycompartment ofthe iigure when the give rise to the phenomena refers toconditions before reaching the point of reversal discussed above.

Having described my invention, what I claim as new and desireito secureby Letters Patent of the United States is:

1. A king pin, a wheel and a brake therefor arranged to turn on saidking pin, a universal joint for operating the brake comprising a firstaxis extending generally transverse to the direction of the king pinaxis and a second axis perpendicular to the first axis, said secondaxis, when the brake is set, being tilted out of the plane perpendicularto the straight forward position of the wheel plane and passing throughthe king pin axis.

2. A king pin, a wheel and a brake therefor arranged to turn on saidking pin, a universal joint for operating the brake comprising a firstaxis extending generally transias ' said second axis,

A king pin, 'a wheel and a brake there-- for arranged to turn on saidking pin, a universal joint for operating the brake comprising a firstaxis extending lgenerally transverse to the direction of. the king pinaxis and a second axis perpendicular to the first 1 axis, said secondaxis, when the brake is set,

being tilted forwardly out of a plane extending transverse to the normaldlrectlon of movement of the wheel and containing the king pin axis.

4. A king pin, a wheel and a brake therefor arranged to turn on'saldking pln, a universal joint for operating the brake eomprlsing a firstaxis extending' generallyl transverse to the direction of the king pinaxls and a second axis perpendicular to the vfirst axis, said secondaxis, when the brake is set, being tilted forwardly relatively to theking pin axis.

5./ A king pin, af wheel and a brake there-- for arranged to turn onsaid king pin, a universal joint for operating the brake comprising afirst axis extending generally transverse to the direction of the kingpin axis and a second axis perpendicular to the first axis, when thebrake is set, being tilted forwardly and outwardly relatively to y theking pin axis.

6. A chassis, a king pin mounted thereon, a wheel anda'brake thereforswiveled on the king pin, a shaft for operatingthe brake, a controlshaft'mounted on the chassis, a universal joint connecting said shaftshaving one of its axis extending upwardly, the said elements being soconstructed and arranged that when the brake is set the said axis istilted forwardly relatively to the king pin ,ax1s.

7. A chassis, a king pin mounted thereon, a wheel and a brake thereforswiveled on the .king pin, a shaft for operating the brake, a

control shaft mounted on the chassis). a u niversal joint connectingsaid shafts having one of its axes extending upwardly,the saidv elementsbeing so constructed and arranged that when the brake is set-the saidaxis is tilted forwardly and outwardlyrelatively to the king pin axis.

8. Thatimprovement inftheart o f setting upswiveledvwheel brakes'operated by a uni-j versal joint connection, which consists insorelating' the brake .and the/universal joint that the act of setting thebrake tilts the upper end yof the upwardly extendintg axis of.

the joint intofa position in fronto he axis around which the wheelswivels.

9. That improvement in the art of setting up swiveled-wheel-brakesoperated by a universal joint connection', which consists in so relatingthe brake and the universal joint.

thatthe act .of setting the brake tilts the upper end of the upwardlyextending axis of the joint into a position infront of the axis aroundwhich the wheel swivels, in accordance with the theory explained in theannexed specification.

10. That improvement in the art of setting up swiveled-wheel brakesoperated by a universal 'jointconnectiom which consists in so relatingthe brake and the universal joint thatl the act of setting the braketilts the upper end of the upwardly extending axis of the joint into aposition in frnt of the axis around which the wheel swivels, invaccordance with the theory explained in the annexed specification, tomake-the brake loosening ei'ect of turning the wheel in one directionaiproximately twice the brake tightening e ect of turning thefwheel inthe opposite direction.

11. Thaty improvement in methods of set-j ting up swiveled wheelbrakesoperated by a universal joint connection which consists in determining,for a given set-up, the position into which the universal joint is to bethrown in setting the brake, by means of Formula (12) of the annexedspecification, and adjusting the brake mechanism so" that the act ofsetting the brake will throw the universal joint into the determinedposition. 12. That improvement in methods of setting up swiveled wheelbrakes-operated by a universal'joint connection which consists indetermining, for a given set-up, the braking effects of throwing thevertical axis of the ]olnt into progressively varying positions, -bymeans of Formula 12), of the annexed specification, selecting thatposition giving the desired relation between inside and outside wheeleffects, and adjusting the brake mechanism to. throw thel vertical axisof the joint to that position in settingthe brake.

13. That improvement in methods of setting up swiveled wheel brakesoperated by a universal joint connection which consists in determining,for a given set-up, the braking effects lcharacteristic. ofprogressively varying angular distances between the king pin axis andthevertical axis .of thejoint when the lbrake is set by means of Formula(12). of the annexed specification andya family of curves derivedtherefrom, as illustrated in Fig. .11 ofthe annexed drawing, selectingthe angular distance characteristic of the desired` vrelation 'betweeninside and outside 'wheel effects, and adjustingthe brake mecha- `nismtothrow the vertical.` to the determined angular king'pin axis insetting the brake.

14. A kin-gy pin, a wheel and a brake therefor arrangedto turn on saidking pin, a universalrjoint for operating-the brake'comprising a `iirstaxis extending generally transverse .to the' direction ofthe king pinaxis and agsecond axis perpendicular to the first axis, said secondaxis, when the brake is set, being tilted out of a plane extendingtransverse to the normal direction of movement of the wheel andcontaining the king pin axisof the joint distance from the.

Y as

' axls, said second amfs, when Athe brake is set,

axis tov an extentl determined means of. the after and before thelrotation.-

vto turn on the' lng Pini 091m. Shaft? Formula (V172) of the 'annexedspecification,

In testimony Awhereof I havesigned my in order to secure a predeterminedrelation .name tothis specificationu outside wheels.

'between the' braking eects on inside and,

wardly toward a vehic e *om which itis mounted,- -awheel and a braketheefo'rar-r 1 varranged to set the brake, a control shaft arinaccordance with the theory explained in tor, and a universal'..jointconecting the cal'n shaft and the control'shaft,1comprising*&

irst axis extending generally .transverse to.'

the direction oithe-king'pin axis and aseo#v ond-axis perpendicular tothe -irst',axis', 1

second` axis, when the brake is set, being tiltedl forwardly andoutwardly. 'relati ely tothe king pinaxis.

j up swiveled-wheelbrakes operated by a 'versa'lloint COIIIGGOD, whichconsists in so" jrelating thV brake andthe universal joint 4thatnthe actof setting the .brake tilts the p u per end ofthe upwardly extendingaxisof t e 'oint into a position in front ando'utsidev of t e axisaround which-the wheel swivels,

the annexed spec cation.

` 17. A kin pin, a wheel and a brake therefor arrange to turn on saidking pin, and a v universal joint for operating the brake com'- prisinga irst axis extending generally'trans-Y verse to the direction of theking pinand a second axis perpendicular to theirst Y being tilted fromthe king pin axis both in a fore and aft direction and in a lateraldirection, relatively to the wheel to secure a predetermined relationbetween the braking effects on the wheel when turned the same amount' tothe right' and to the left respectively, the position of the said secondaxis when the brake isset, and the eects of sald position on the saidbraking ei'fects being. de-

termined by the following formulal axis, referred to a system ofcartesian co-ordmates,' Z, m, n, are the direction cosines of I the kingpin axis, and (w1, y1, el) and (my, z)

are the (zo-ordinates of any selected point of vai) CertificateCorrection `v p .Patent N o. 1,749,022.v l Granted March 4, 1930, to

ADIEL Y. DODGE v It is herebyoertied that error appears in the printedspecification of the above numbered patent requiring correction asfollows: Page 1, line 14, strike out the comma after the word somewhatand insert the same after backward, page 2,

` line 13, after hereinfinsert a semicolon; page 5, lines 111 to 114,strike out the equations and insert instead i: y: ,y--tanoz z ,tan .xtanfy, l page 6, line 19, u1/1 n2. should read 1/1 'n2, line 23 lforFormula (16) gives read Formul (16) give; and line 67 for i, m, n readl, m, ni page .7, line 67, for x1 read w; page 8, llnes l to 4, strikeout the equations and insert lnstead cOt2a= 0.0019063 tanz 0.0110469 1same page, lines 12 to 15, str ike out the equations and insertc0t2v=0.0003047 tanz'y 0.0012195 same age, line 37, strike out S0 andinsert s0;1ine v53, in the equation the shoul be raised to the fractionline; and line 97, strike out the numeral 9 at the end of the firstfraction; page 9, line 1, =0 should read -'0;}pag'e 10, lines 40 and 56,for the minus sign read page 12, line 35, claim 6, for axis read'axes;and that the said Letters Patent should be read with these correctionstherein that the same may conform to the-record of the case in thePatent OIice. Y

Signed and sealed this 1st day of July, A. D. 1930.

[SEAL] M. J'. MOORE,

Acting Commissioner Qf Patents.

